Time-domain System Identification Research Articles

Damage assessment of shear buildings by synchronous estimation of stiffness and damping using measured acceleration

Nonlinear time-domain system identification (SI) algorithm is proposed to assess damage in a shear building by synchronously estimating time-varying stiffness and damping parameters using measured acceleration data. Mass properties have been assumed as the a priori known information. Viscous damping was utilized for the current research. To chase possible nonlinear dynamic behavior under severe vibration, an incremental governing equation of vibrational motion has been utilized. Stiffness and damping parameters are estimated at each time step by minimizing the response error between measured and computed acceleration increments at the measured degrees-of-freedom. To solve a nonlinear constrained optimization problem for optimal structural parameters, sensitivities of acceleration increment were formulated with respect to stiffness and damping parameters, respectively. Incremental state vectors of vibrational motion were computed numerically by Newmark-<TEX>${\beta}$</TEX> method. No model is pre-defined in the proposed algorithm for recovering the nonlinear response. A time-window scheme together with Monte Carlo iterations was utilized to estimate parameters with noise polluted sparse measured acceleration. A moving average scheme was applied to estimate the time-varying trend of structural parameters in all the examples. To examine the proposed SI algorithm, simulation studies were carried out intensively with sample shear buildings under earthquake excitations. In addition, the algorithm was applied to assess damage with laboratory test data obtained from free vibration on a three-story shear building model.

System identification of suspension bridge from ambient vibration response

The paper addresses and evaluates the application of system identification to a suspension bridge using ambient vibration response. To obtain dynamic characteristics of the bridge, two output-only time-domain system identification methods are employed namely, the Random Decrement Method combined with the Ibrahim Time Domain (ITD) method and the Natural Excitation Technique (NExT) combined with the Eigensystem Realization Algorithm (ERA). Accuracy and efficiency of both methods are investigated, and compared with the results from a Finite Element Model. The results of system identification demonstrate that using both methods, ambient vibration measurement can provide reliable information on dynamic characteristics of the bridge. The NExT-ERA technique, however, is more practical and efficient especially when applied to voluminous data from multi-channel measurement. The results from three days of measurements indicate the wind-velocity dependency of natural frequency and damping ratio particularly for low-order modes. The sources of these dependencies appear to be the effect of aerodynamic forces alongside the girder, and friction force from the bearing near the towers.

Physical interpretation of independent component analysis in structural dynamics

This paper focuses on the relation between the vibration modes of mechanical systems and the modes computed through a blind source separation technique called independent component analysis (ICA). For free and random vibrations of weakly damped systems, a one-to-one relationship between the vibration modes and the ICA modes is demonstrated using the concept of virtual source. Based on this theoretical link, a time-domain structural system identification technique is proposed and is illustrated using numerical examples.

Defect identification under uncertain blast loading

A novel finite element-based system identification procedure is proposed to detect defects in existing frame structures when excited by blast loadings. The procedure is a linear time-domain system identification technique where the structure is represented by finite elements and the input excitation is not required to identify the structure. It identifies stiffness parameter (EI/L) of all the elements and tracks the changes in them to locate the defect spots. The similar procedure can also be used to monitor health of structures just after natural events like strong earthquakes and high winds. With the help of several numerical examples, it is shown that the algorithm can identify defect-free and defective structures even in the presence of noise in the output response information. The accuracy of the method is much better than other methods currently available even when input excitation information was used for identification purpose. The method not only detects defective elements but also locate the defect spot more accurately within the defective element. The structures can be excited by single or multiple blast loadings and the defect can be relatively small and large. With the help of several examples, it is established that the proposed method can be used as a nondestructive defect evaluation procedure for the health assessment of existing structures.

A weighted-principal component regression method for the identification of physiologic systems

We introduce a system identification method based on weighted-principal component regression (WPCR). This approach aims to identify the dynamics in a linear time-invariant (LTI) model which may represent a resting physiologic system. It tackles the time-domain system identification problem by considering, asymptotically, frequency information inherent in the given data. By including in the model only dominant frequency components of the input signal(s), this method enables construction of candidate models that are specific to the data and facilitates a reduction in parameter estimation error when the signals are colored (as are most physiologic signals). Additionally, this method allows incorporation of preknowledge about the system through a weighting scheme. We present the method in the context of single-input and multi-input single-output systems operating in open-loop and closed-loop. In each scenario, we compare the WPCR method with conventional approaches and approaches that also build data-specific candidate models. Through both simulated and experimental data, we show that the WPCR method enables more accurate identification of the system impulse response function than the other methods when the input signal(s) is colored.

Health Assessment at Local Level with Unknown Input Excitation

A finite-element-based procedure is proposed to identify defects in existing structures and evaluate their extent at the local element level for the purpose of health assessment. The procedure is a time-domain system identification technique where input excitation is not required to identify a structure. It estimates the dynamic properties of a structure in terms of stiffness and damping at the element level in a finite-element representation. The method can be used to precisely locate a defective spot in an element. Although input excitation information is not required, examples are used to show that the algorithm is robust enough to identify a structure excited by different types of loading. Structures can be excited simultaneously by multiple loadings, and the response information can be noise-free or noise-contaminated. Defects can be small or relatively large. In all cases, the algorithm identified the structures correctly. The error in the identification is considerably smaller than that of other available methods where input excitation information is used to identify a structure. With the help of examples, it is shown that the algorithm can potentially be used as a nondestructive evaluation technique for health assessment of existing structures with minimum disruption of operations. Since the procedure is very simple and requires only a few seconds of response information, it is expected to be very economical and efficient.

Structural system identification in time domain using measured acceleration

This paper presents a system identification scheme in time domain to estimate stiffness and damping parameters of a structure using measured acceleration. An error function is defined as the time integral of the least-squared errors between measured accelerations and calculated accelerations by a numerical model of a structure. To alleviate the ill-posedness of SI problems a regularization technique is employed and a new regularization function for the time-domain SI is proposed. The regularization factor is determined by the geometric mean scheme. The validity of the proposed method is demonstrated by a numerical simulation study on a two-span truss bridge and by an experimental laboratory study on a three-story shear building model.

측정 가속도 증분을 사용한 비선형 SI 기법의 개발

구조물의 손상 진단을 위해 측정 가속도 데이터를 사용한 비선형 시간영역 SI 알고리듬을 개발하였다. 구조물의 비선형 거동을 고려하기 위하여 측정 가속도 증분과 해석에 의한 가속도 증분의 차이로 출력오차를 정의하고, 구속 비선형 최적화 문제를 풀어 최적 구조변수를 구하였다. 개발된 알고리듬은 시간에 따라 변하는 강성도와 감쇠 변수를 추정하도록 하였다. 구조물의 비선형 거동에 의한 복원력은 추정된 시간에 따라 변하는 구조변수와 Newmark-<TEX>$\beta$</TEX>법으로 계산한 변위를 사용하여 복원하였으며, 복원 과정에서 비탄성 거동에 대한 어떤 모델도 사전에 설정하지 않았다. 개발한 알고리듬에서는 측정오차와 공간 및 상태에 대한 불완전 측정의 경우를 고려하였다. 개발한 알고리듬을 검증하기 위하여 3층 전단건물에 대한 수치 모의시험과 실내 모형실험을 통한 연구를 수행하였다. A nonlinear time-domain system identification algorithm using measured acceleration data is developed for structural damage assessment. To take account of nonlinear behavior of structural systems, an output error between measured and computed acceleration increments has been defined and a constrained nonlinear optimization problem is solved for optimal structural parameters. The algorithm estimates time-varying properties of stiffness and damping parameters. Nonlinear response of restoring force of a structural system is recovered by using the estimated time-varying structural properties and computed displacement by Newmark-<TEX>$\beta$</TEX> method. In the recovery, no pre-defined model for inelastic behavior has been assumed. In developing the algorithm, noise and incomplete measurement in space and state have been considered. To examine the developed algorithm, numerical simulation and laboratory experimental studies on a three-story shear building have been carried out.

Application of a Web-enabled real-time structural health monitoring system for civilinfrastructure systems

The system architecture of a novel structural health monitoring system that isoptimized for the continuous real-time monitoring of dispersed civil infrastructures ispresented. The monitoring system is based on a highly efficient multithreaded softwaredesign that allows the system to acquire data from a large number of channels,monitor and condition this data, and distribute it, in real time, over the Internet tomultiple remote locations. Bandwidth and latency issues that impact the operationof monitoring systems are discussed. The application of the monitoring systemunder discussion to a long span, flexible bridge in the metropolitan Los Angelesregion is described. The bridge had previously been instrumented with 26 strongmotion accelerometers. Sample ‘quick analysis’ results continuously provided by themonitoring system are presented and interpreted. System identification results,obtained through off-line batch processing, are presented for a data set from arecent earthquake that automatically triggered the recording capability of thesystem. It is shown that, using a time domain system identification approach,the bridge stiffness and damping matrices can be identified from the earthquakedata set and subsequently used to determine the bridge modal properties, suchas frequencies and damping ratios. In this approach the bridge is modeled as amulti-input/multi-output system with order compatible with the number of availablesensors. Implementation issues requiring further investigation are presented and discussed.

Active Vibration Control and Fault Detection of Smart Structures(International Workshop on Smart Materials and Structural Systems, W03 Jointly organized by Material &amp; Processing Division, Material &amp; Mechanics Division, Dynamics &amp; Control Division and Space Engineering Division.)

Experimental researches on active control of smart structures with piezoelectric actuators have been conducted in the laboratory. The major objective of the researches is to develop a robust and reliable control system for smart structures considering system uncertainties such as structural parameter errors and system failures. Two topics are introduced in this paper. One is the study on a discrete-state sliding mode control (SMC) for vibration control of smart structures. The discrete-state subspace system identification (4SID) is used in combination with the discretestate SMC design, and a software module for seamless transformation from discrete system to continuous system has been developed. The proposed discrete-state sliding mode control has been applied to the flexible cantilever beam equipped with a piezoelectric actuator. It is shown both by numerical simulations and by hardware experiments that the discrete-state SMC has high performance of vibration suppression and robustness against system uncertainties. The second topic is a new method for the fault detection and health monitoring of smart structures. The Eigensystem Realization Algorithm (ERA), a time-domain system identification algorithm, is applied to detect system failures by monitoring the estimated eigenvalues of the system matrix. The ERA is a powerful tool for detecting the small variation in the stifftiess parameter that indicates a structural damage.

Wavelet Transforms for System Identification in Civil Engineering

Abstract: The time‐frequency character of wavelet transforms allows adaptation of both traditional time and frequency domain system identification approaches to examine nonlinear and non‐stationary data. Although challenges did not surface in prior applications concerned with mechanical systems, which are characterized by higher frequency and broader‐band signals, the transition to the time‐frequency domain for the analysis of civil engineering structures highlighted the need to understand more fully various processing concerns, particularly for the popular Morlet wavelet. In particular, as these systems may possess longer period motions and thus require finer frequency resolutions, the particular impacts of end effects become increasingly apparent. This study discusses these considerations in the context of the wavelet's multi‐resolution character and includes guidelines for selection of wavelet central frequencies, highlights their role in complete modal separation, and quantifies their contributions to end‐effect errors, which may be minimized through a simple padding scheme.

Damage Identification of Structural Members: Numerical and Experimental Studies

The main objective of the study is to formulate a numerical strategy suitable for structure member assessment in a quantifiable and objective way. Involving both numerical and experimental studies, the emphasis is on nondestructive damage detection of structural members with predominantly flexural deformations such as beams and columns. A time-domain system identification method, namely the extended Kalman Filter method, is adopted with some modifications. To reduce the identification system nonlinearity and hence improve the convergence performance, the method of stiffness-damping uncoupling is introduced. Flexural members with semirigid connections are modeled by the finite element method. Local damage is assumed to manifest itself as reduction in flexural rigidity. Numerical simulation study is carried out to illustrate the performance of the damage identification strategy, accounting for the effects of measurement noise. Dimensionless indicators are used to reveal the damage location and severity effectively. The problem of numerical leakage is reduced, by comparing average identification results before and after damage. Lastly, an experimental study for a reinforced concrete beam with controlled change in local stiffness further substantiates the feasibility of the proposed strategy.

A feasibility study of on-line excitation system parameter estimation

This paper details a feasibility study of estimating excitation system parameters during online operation using time-domain system identification. This study concentrates on identifying the appropriate exciter model, developing an input signal that would provide a proper level of perturbation such that the dynamics of the system can be captured, analyzing the effects of both systematic and random noise, developing algorithms to perform the parameter estimation, testing and validating the obtained system parameters. This study established a strong basis for estimating the system parameters during online operation.

System Identification with Limited Observations and without Input

A time domain system identification technique is proposed to estimate the stiffness and damping parameters, at the element level, of a structure excited by unknown or unmeasured input forces. The unknown input forces could be of any type, including seismic loading. The unique feature of this technique is that it does not require response measurements at all dynamic degrees of freedom of the structure. This new procedure is a combination of an iterative least-squares procedure with unknown input excitations (ILS-UI) proposed earlier by the writers, and the extended Kalman filter method with a weighted global iteration (KF-WGI). The new procedure is denoted by the writers as ILS-EKF-UI. The uncertainty in the output responses is considered, and its effect on the accuracy of the identified parameters is analyzed. The efficiency, accuracy, and robustness of the proposed algorithm are illustrated by numerical examples. The accuracy of the proposed ILS-EKF-IU procedure is of the same order as that of ILS-UI; however, it requires a longer response measurement. This is expected, since ILS-EKF-UI identifies a structure using less information than the ILS-UI does. However, the efficiency of the new algorithm can be improved by considering a shorter duration of response measurements for the ILS-UI procedure and a longer duration for the KF-WGI without compromising the accuracy of the identified parameters.

ANALYSIS OF NONLINEAR SYSTEM USING NARMA MODELS

The purpose of this paper is to develop a systematic method of time-domain nonlinear system identification using NARMA model. In the beginning the Hilbert transform test was used for nonlinearity, then an orthogonal parameter estimation algorithm is applied to a NARMA model which represents the nonlinear system model. Finally the nonlinear frequency response functions were computed. Application of the methodology to a combined Duffing and Van Der Pol nonlinear system and the seismic response data of Van Nuys building to Whittier and Northridge earthquakes are studied.

Evaluation of dynamic characteristics of high-rise buildings using system identification techniques

Among many estimation methods of modal parameters of structures, system identification methods in the time domain have recently been spotlighted. System identification methods in the time domain have advantages over the methods in the frequency domain in such cases where the modal parameters are changed during the records or where the length of the record is very short. In this paper, dynamic characteristics, including natural frequencies and damping ratios, of twin high-rise buildings are estimated by applying time domain system identification methods to the records of their earthquake responses.

Element‐Level System Identification with Unknown Input

A finite element‐based time domain system identification procedure is proposed to evaluate existing large structural systems at the element level. The procedure does not need any information on the input excitation forces. Since the input exciting forces are not required, there is no restriction on the type of exciting force, only a small number of observation time points are required and no information is required on the modal properties of the structure. The unknown exciting forces can be applied at the ground level representing the seismic excitation. The procedure is particularly applicable to identifying an existing structure. The method is verified using three examples. For verification purposes, both the noise‐free and noise‐included output responses are considered. In all cases, the proposed method identified the structural parameters very well. The errors in the estimation of the parameters are considerably smaller than those in the other methods currently available in the literature. The propose...

Frequency Domain System Identification Toolbox for MATLAB

Abstract A frequency domain system identification package is described, written in MATLAB. The whole experiment design and evaluation procedure is supported: excitation signal optimization (binary and arbitrary waveforms), data preprocessing and variance analysis, parameter estimation via nonlinear least squares fitting in the frequency domain, model validation, transfer function and pole/zero plots with uncertainties, simulations. The results can be matched to those of the time domain SYSTEM IDENTIFICATION TOOLBOX, also available for MATLAB.

Identification of time varying modal parameters

AbstractThe ability to track time varying frequency and damping parameters using on-line versions of seven time domain system identification algorithms; Least Squares, Double Least Squares, Correlation Fit, Instrumental Variables, Instrumental Matrix with Delayed Observations, Extended Least Squares and Maximum Likelihood, is examined. Comparisons are made on results obtained from data generated from various simulated time varying systems, corrupted with both input and measurement noise, as a preliminary step before advancing onto real data. Only the Maximum Likelihood and Double Least Squares methods gave acceptable results on the most difficult data sets that were considered. The choice of an exponential weighting factor is crucial to the performance of the on-line methods when applied to data from time varying systems. The effect of assigning various values of the weighting factor is demonstrated. Further work is required to determine the optimum schemes for defining this parameter.

Real‐Time System Identification of Degrading Structures

On-line identification becomes an important issue when structures undergo nonlinear and time-dependent degrading behavior under large loads. In this paper, a real-time, time-domain system-identification technique is developed to identify time-varying system parameters for a multidegree-of-freedom degrading structure subjected to general dynamic loads, such as earthquakes. A system of second-order, linear, ordinary differential equations with time-varying system parameters is solved to generate the system response using the Newmark time-integration method. Gaussian white noise is added to the response and the results are used to simulate the measurements. Then, a least-square’s method is employed to estimate the system parameters in real time based on input data and corresponding response measurements with or without noise. Two numerical examples, a single-degree-of-freedom and a three-degree-of-freedom structure subjected to a simulated El Centro earthquake, are considered. The changes in structural stiffnesses for the example problems are identified. Encouraging results are obtained for both cases.